8.3 Processing steps 8.3.7 Spectrophotometry processing 8.4 Quality assessment and validation

8.3.8 Error model for Spectrophotometry

Author(s): Laurent Galluccio, Marco Delbó

The uncertainties of the spectral reflectance values for the SSOs were calculated using error propagation throughout the entire process of computation of the final reflectance. The first step concerned the error of the epoch reflectance $\sigma_{R(\lambda_{i})}$ :

$\sigma_{R(\lambda_{i})_{t}}=|R(\lambda_{i})_{t}|\sqrt{\left(\frac{\sigma_{f(% \lambda_{i})_{t}}}{f(\lambda_{i})_{t}}\right)^{2}+\left(\frac{\sigma_{F(% \lambda_{i})}}{F(\lambda_{i})}\right)^{2}}.$

(8.24)

In the second step, when the reflectance spectra were normalized using the $\xi_{t}$ factor, the errors were updated accordingly:

$\sigma_{R(\lambda_{i})_{t}}=|R(\lambda_{i})_{t}|\sqrt{\left(\frac{\sigma_{R(% \lambda_{i})_{t}}}{R(\lambda_{i})_{t}}\right)^{2}+\left(\frac{\sigma_{\xi_{t}}% }{\xi_{t}}\right)^{2}}.$

(8.25)

The third step of error propagation was related to the computation of the mean reflectance spectrum. At each wavelength band, when computing the weighted average spectrum, its error was also calculated:

$\sigma_{R(\lambda_{i})}=\left(\sqrt{\sum_{i=1}^{N}\frac{1}{\sigma_{R(\lambda_{% i})_{t}}^{2}}}\right)^{-1}.$

(8.26)

The final step of error propagation concerned the normalization at $\lambda=550$ nm:

$\sigma_{R(\lambda_{i})}=|R(\lambda_{i})|\sqrt{\left(\frac{\sigma_{R(\lambda_{i% })}}{R(\lambda_{i})}\right)^{2}+\left(\frac{\sigma_{R(550)}}{R(550)}\right)^{2% }}.$

(8.27)

The information is given in the archive for each SSO and wavelength in the table sso_reflectance_spectrum in the field reflectance_spectrum_err.

gaia data release 3 documentation

8.3.8 Error model for Spectrophotometry